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Formation of Stars and Planets Frank H. Shu National Tsing Hua University Arnold Lecture – UC San Diego 6 May 2005 Outline of Talk • • Origin of solar system – review of classical ideas Modern theory of star formation – – – – – – – Four phases of star formation Contraction of molecular cloud cores Gravitational collapse and disk formation The initial mass function X-wind outflow and YSO jets The inner disk edge Migration of planets Planets Revolve in Mostly Circular Orbits in Same Direction as Sun Spins Planetary Orbits Nearly Lie in a Single Plane with Exception of Pluto & Mercury Laplace’s Nebular Hypothesis Photo Credit: NASA/JPL Snowline in the Solar Nebula Rocks and metals stay condensed, hydrogen compunds vaporize. Hydrogen compounds, rocks, and metals stay condensed. Relative Abundance of Condensates Agglomeration of Planets The Formed Solar System Four Phases of Star Formation • Formation of recognizable cores in Giant Molecular Cloud (GMC) by ambipolar diffusion (AD) and decay of turbulence: Δt = 1 – 3 Myr • Rotating, magnetized gravitational collapse: Δt = ? • Strong jets & bipolar outflows; reversal of gravitational infall: Δt = 0.1 – 0.4 Myr • Star and protoplanetary disk with lifetime: Δt = 1 – 5 Myr Shu, Adams, & Lizano (1987) Equations of Non-Ideal MHD for an Isothermal Gas u 0, t u a2 1 1 2 u ( u ) u U B B, t 4 2 2U 4G , B B ( B u ) B B ( B) , t 4 with a 2 kT / m const and (electrica l resistivit y) and (neutral - ion collision time) specified by microphysi cs. Neutral - ion collision time is greatly increased when region is shielded from UV ionization (perpendic ular AV 4 mag). Ideal MHD correspond s to 0 and 0. Cloud-Core Evolution by Ambipolar Diffusion t = 7.1 Myr 15.17 Myr Displayed time scale for laminar evolution is in conflict with statistics of starless cores versus cores with stars by factor of 3 - 10 (Lee & Myers1999; Jajina, Adams, & Myers 1999). 15.23189 Myr 15.23195 Myr → Reset to 0 (pivotal state). Turbulent decay (Myers & Lazarian 1999) and turbulent diffusion (Zweibel 2002, Fatuzzo & Adams 2002) may reduce actual time to 1 - 3 Myr. Desch & Mouschovias (2001). See also Nakano (1979); Lizano & Shu (1989). Pivotal t = 0 States: Magnetized Singular Isothermal Toroids AD leads to gravomagneto catastrophe, whereby center formally tries to reach infinite density in finite time – seems to be nonlinear attractor state with ρ~1/r², B~1/r, Ω~1/r. If we approximate the pivotal state as static, it satisfies a2 4a 2 r (r , ) R( ), (r , ) 1/ 2 ( ) with 2 2Gr G 1 d ' R ' sin 2 H 0 2R 1 H 0 , sin d R d ' H 0 R sin . d sin /2 0 R( ) sin d 1 H 0 . N.B. solution for H 0 = 0: R = 1, Φ= 0 (Shu 1977). Magnetic Isodensity contours field lines Li & Shu (1996) Collapse of H0 = 0.0, 0.125, 0.25, 0.5 Toroids Case H 0 = 0 agrees with known analytical solution for SIS (Shu 1977) or numerical simulations without B (Boss & Black1982). Formation of pseudodisk when H0 > 0 as anticipated in perturbational analysis by Galli & Shu (1993). Note trapping of field at origin produces split monopole with long lever arm for magnetic braking. Mass infall rate into center: M 0.975 (1 H 0 )a 3 / G Allen, Shu, & Li (2003) gives 0.17 Myr to form 0.5 Msun star. Mass infall rate doubled if there is initial inward velocity at 0.5 a. Catastrophic Magnetic Braking if Fields Are Perfectly Frozen Low-speed rotating outflow (cf. Uchida & Shibata 1985) not high- speed jet Andre, Motte, & Bacmann (1999); also Boogert et al. (2003) Allen, Li, & Shu (2003) – Initial rotation in range specified by Goodman et al. (1993). Some braking is needed, but frozen-in value is far too much (no Keplerian disk forms). Breakdown of Ideal MHD • Low-mass stars need 10 megagauss fields to stop infall from pseudodisk by static levitation (if envelope subcritical). • Combined with rapid rotation in a surrounding Keplerian disk, such stars need only 2 kilogauss fields to halt infall by X-winds (dynamical levitation). • Appearance of Keplerian disks requires breakdown of ideal MHD (Allen, Li, & Shu 2003; Shu, Galli, & Lizano 2005). • Annihilation of split monopole is replaced by multipoles of stellar field sustained by dynamo action. • Latter fields are measured in T Tauri stars through Zeeman broadening by Basri, Marcy, & Valenti (1992) and Johns-Krull, Valenti, & Koresko (1999). Computed Steady X-Wind Filling All Space Apart from details of mass loading onto field lines, only free parameters are M , M , . D fM M w D f 1 J* D 1 J w J* 3 v w 2 J w 3 x Rx 1/ 7 4 , Rx 0.923 2 GM M D 1/ 2 GM * x 3 , Rx x (disk locking). Ostriker & Shu (1995) Najita & Shu (1994) Multipole Solutions Change Funnel Flow but not X-wind Mohanty & Shu (2005) What’s important is trapped flux at X-point (Johns-Krull & Gafford 2002). Prototypical X-Wind Model (1 Rx 0.06 AU typically ) Alfven fast slow streamline isodensity contour Shu, Najita, Ostriker, & Shang (1995) Gas: YSO Jets Are Often Pulsed Magnetic Cycles? Shang, Glassgold, Shu, & Lizano (2002) Synthetic Long-Slit Spectra i 90 i 60 i 30 velocity (km/s) Shang, Shu, & Glassgold (1998) Position-Velocity Spectrogram Jet/Counterjet R W Tauri Woitas, Ray, Bacciotti, Davis, & Eisloffel (2002) LV2 Microjet in Orion Proplyd Henney, O’Dell, Meaburn, & Garrington (2002) Relationships Among Core Mass, Stellar Mass, & Turbulence • • • Conjecture: Outflows break out when infall weakens and widens after center has accumulated some fraction (50%?) of core mass (1/3 of which is ejected in X-wind). Physical content of Class 0? (Andre, Ward-Thompson & Barsony 1993) Stellar mass is therefore defined by X-wind as 1/3 of core mass M 0 m0 (a 2 v 2 ) 2 / G 3 / 2 B0 . Distributi on of m0 2 . Ambipolar diffusion and turbulence driven by outflows lead to distribution of (a 2 v 2 ) 2 / B0 that yields core mass function. Shu, Li, & Allen (2004) 1 (r0) above is 200,000 times bigger than 1 (Rx) below Shang, Ostriker, & Shu (1995) Attack by matched asymptotic expansions Core Mass with Magnetic Fields and Turbulence • Pivotal state produced by AD (Mestel & Spitzer 1956, Nakano 1979, Lizano & Shu 1989, Basu & Mouschovias 1994, Desch & Mouschovias 2004): 2G1/ 2 M 0 Core mass: 2. 2 part which is supercritical r0 B0 • Virial equilibrium: 2 Differs from barely GM 3 2 2 0 . 2 M 0 (a v ) bound in factor 2. 2 r0 • Solve for 2 2 2 2 2 M0 9(a v ) 3(a v ) , r . 0 3/ 2 1/ 2 G B0 G B0 • Compare with SIS threaded by uniform field: M0 2a 4 G 3/ 2 B0 , r0 a 2 1/ 2 G B0 . M 0= 1.5 solar mass for a = 0.2 km/s, B = 30μG 0 Divide mass by 4 if barely bound Simple “Derivation” for IMF 2 2 when v >> a 2 Bipolar outflows : (v)dv v dv . (Shu, Ruden, Lada, & Lizano 1990; Masson & Chernin 1992; Li & Shu 1996) m0v 4 1 3 When v a : M * M 0 v . 3/ 2 3 3G B0 2 2 m0v r0 M * m0v 4 / 3G 3 / 2B0 5 tsf 1 4 10 yr (Myers & Fuller 1993) 3 1/ 2 M* (2 / 3)v / G 2G B0 2v M * ( M * )dM * F 4 / 3 (v)dv M * dM * , 3 (Shu, Li, & Allen 2004) which is Salpeter IMF at intermedia te masses (peak at 2 a 4 /3G 3 / 2 B0 0.5 M sun ; steeper at high stellar masses because of radiation pressure on dust grains). NB: SFE = 1/3 when F = 1 (cf. Lada & Lada 2003). Schematic IMF Log [MN(M)] H fusion wind brown dwarf - 4/3 slope wind wind Motte et al. (1998, 2001); v<a Testi & Sargent (1998) radiation stars pressure cores D fusion m0 distribution -1 0 +1 +2 Log (M) +3 +4 The Orion Embedded Cluster Trapezium Cluster Initial Mass Function Sun HBL 102.09 At stellar 8 7 6 5 birth (Lada & Lada 2003), Log N + Constant 4 3 IMF is 2 given by Salpeter (1955) IMF. 101.09 8 7 6 5 4 Brown Dwarfs 3 2 100.0 1.5 1.0 0.5 0.0 -0.5 -1.0 Log Mass (solar masses) -1.5 -2.0 Almost 100% of Young Stars in Orion Cluster Are Born with Disks Discovery of Extrasolar Planets Marcy webpage Driven Spiral Density and Bending Waves in Saturn’s Rings Shu, Cuzzi, & Lissauer (1983) Implications for planet migration due to planet-disk interaction Shepherd Satellites Predicted by Goldreich & Tremaine Photo credit: Cassini-Huygens/NASA Model Fit to CO Fundamental (v = 1→0, ΔJ = 1) Inferred gas temperature ≤ 1200 K; kinematics gives location of inner disk edge. Najita et al. (2003) Is this where oxygen isotope ratios are fixed? (Clayton 2002) Size of Inner Hole in Rough Agreement with Disk Locking Najita et al (2003) Parking Hot Jupiters Thank you, everyone!